It is strange for an ipad2 to be happening so much. You say you close your apps completely too which makes it even stranger. When was the last time you did a restart and reset. Doing a restart occasionally is a good idea, and if your iPad is behaving strangely as yours is a reset is also a very good idea.
Restart: Press and hold the power off button, the one at the top right. You will see a slide appear to power off, slide this and the screen will go dark and a Whirly will appear. When the Whirly disappears your iPad is now off. Press the power button again until the Apple logo appears, this will take a few seconds and your iPad will restart. You should restart your iPad occasionally also as it will keep it running well. Now see if it is operating. If not a reset is the next step.
Reset: Hold the power off button and the home button simultaneously, keep holding them in and you will see the power off slide appear and disappear, wait until you see the Apple logo appear before releasing the buttons. It will take a little longer for your iPad to start.
You may even find your iPad being a little more responsive after a reset. Let us know how you go.